# Edexcel Core Mathematics C4 June 2011

These video lessons with Questions and Worked Solutions are for C4 Edexcel Core Mathematics June 2011 (Part 2).

Edexcel Core Mathematics C4 June 2011 Past Paper

C4 Mathematics Edexcel June 2011 Question 6

1. With respect to a fixed origin O, the lines l1 and l2 are given by the equations.
where λ and μ are scalar parameters. (a) Show that ll and l2 meet and find the position vector of their point of intersection A.

(b) Find, to the nearest 0.1°, the acute angle between l1 and l2

The point B has position vector

(c) Show that B lies on l1

(d) Find the shortest distance from B to the line l2, giving your answer to 3 significant figures.

6. (a) Vectors

1. (b) Vectors

1. (c)
1. (d)

C4 Mathematics Edexcel June 2011 Question 7

Figure 3 shows part of the curve C with parametric equations
x = tanθ, y = sinθ , 0 ≤ θ < π/2

The point P lies on C and has coordinates (√3, ½√3)

(a) Find the value of ș at the point P.

The line l is a normal to C at P. The normal cuts the x-axis at the point Q.

(b) Show that Q has coordinates (k√3, 0) , giving the value of the constant k.

The finite shaded region S shown in Figure 3 is bounded by the curve C, the line x = √3 and the x-axis. This shaded region is rotated through 2π radians about the x-axis to form a solid of revolution.

(c) Find the volume of the solid of revolution, giving your answer in the form pπ√3 + qπ2, where p and q are constants.

1. (a) Parametric equations
1. (b) Normal to a Parametric Curve

1. (c) Volume of Revolution to a Parametric Curve

C4 Mathematics Edexcel June 2011 Question 8

1. (a) Find ∫(4y + 3)-1/2 dy

(b) Given that y =1.5 at x = – 2, solve the differential equation
dy/dx = √(4y + 3)/x2

1. (a) Integration methods

1. (b) Differential Equations

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